Abstract
We present a derivation and efficient implementation of the formally complete analytic second derivatives for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory (MP2) method, applicable to electric or magnetic field-response properties but not yet to harmonic frequencies. We also discuss the occurrence and avoidance of numerical instability issues related to singular linear equation systems and near linear dependences in the projected atomic orbital domains. A series of benchmark calculations on medium-sized systems is performed to assess the effect of the local approximation on calculated nuclear magnetic resonance shieldings and the static dipole polarizabilities. Relative deviations from the resolution of the identity-based MP2 (RI-MP2) reference for both properties are below 0.5% with the default truncation thresholds. For large systems, our implementation achieves quadratic effective scaling, is more efficient than RI-MP2 starting at 280 correlated electrons, and is never more than 5-20 times slower than the equivalent Hartree-Fock property calculation. The largest calculation performed here was on the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions and took 3.3 days on 12 central processing unit cores.
Highlights
The early development of local electron correlation methods is due to Pulay and Sæbø,[1,2,3] and thanks to recent advancements in several research groups,[4–41] the popularity and applicability of these methods for the calculation of relative energies have grown tremendously
Another study by Werner and co-workers examines the accuracy of projected atomic orbitals (PAOs)-based local correlation methods for polarizability calculations via finite differences,[57] an approach that is difficult to apply to magnetic properties as it requires an implementation based on complex algebra
We present a derivation of analytic second derivatives of domain-based local pair natural orbital (DLPNO)-MP2, applicable to field-response properties, such as dipole polarizabilities and nuclear magnetic resonance (NMR) shieldings
Summary
The early development of local electron correlation methods is due to Pulay and Sæbø,[1,2,3] and thanks to recent advancements in several research groups,[4–41] the popularity and applicability of these methods for the calculation of relative energies have grown tremendously. Considering the massive progress that has been made in this field for the calculation of electronic energies, there are comparatively few works that make use of local correlation approximations to compute molecular properties This is, in part, because many observable properties—such as the dipole moment and polarizability, nuclear magnetic resonance. The present work extends their applicability to much larger systems and should be viewed as part of an ongoing effort to reduce the computational cost of MP2 response property calculations Works in this context are the integral-direct gaugeincluding atomic orbital (GIAO) MP2 implementation for shieldings of Kollwitz, Häser, and Gauss,[74,75] the derivation of RI-MP2 second derivatives in combination with chain-of-spheres exchange (COSX),[76] the Laplace-based approaches of Ochsenfeld, Hättig, and their co-workers,[25,59] the proof-of-concept GIAO-LMP2 implementation,[54] and, in particular, the efficient RI-based version of the latter.[55,56]. Works in this context are the integral-direct gaugeincluding atomic orbital (GIAO) MP2 implementation for shieldings of Kollwitz, Häser, and Gauss,[74,75] the derivation of RI-MP2 second derivatives in combination with chain-of-spheres exchange (COSX),[76] the Laplace-based approaches of Ochsenfeld, Hättig, and their co-workers,[25,59] the proof-of-concept GIAO-LMP2 implementation,[54] and, in particular, the efficient RI-based version of the latter.[55,56] Note that the present derivation and implementation are not applicable to harmonic vibrational frequencies, as the efficient evaluation of the nuclear Hessian requires a substantially different algorithm
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